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After a couple of false starts, the conversion Tolkien wound up making was March 1 = March 1, with the rest of the calendar extended before and after that pivot-point or fulcrum. In other words, if you were to back-convert Appendix B to Gregorian using either your suggested method, or the 'canonical' Jan 1 = 2 Yule, you won't recreate the Gregorian dates he actually used when writing the book.
There were a couple of reasons why he did so (and he even, for once, left a note), but the primary one was to ensure that Sauron's fall remained on March 25.
OTOH, he had to add a couple of days to the journey from Rivendell to Hollin, to retain the Departure on December 25. While Tolkien was not one to smack the reader in the face with Christian allusions a la Lewis, nonetheless they are in there.
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The entire plot of The Lord of the Rings could be said to turn on what Sauron didn’t know, and when he didn’t know it.
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